Experiment on the constitutive model of fiber reinforced concrete with volume fraction of alkali-resistant glass fiber of, respectively, 0.0%, 0.5%, 1.0%, and 1.5% was conducted, and the constitutive relation of tension stress-strain full curve of GFRC shaft was obtained; the constitutive relation of GFRP is obtained by experiment, and the secant modulus was obtained by the fitting of univariate cubic equation. The finite element numerical simulation of GFRP fiber reinforced concrete beam was carried out, and the load deflection nephogram of fiber reinforced concrete beam, strain nephogram, crack nephogram, and GFRP stress nephogram were obtained. When the fiber content is 1.0%, the bearing capacity of GFRP reinforced concrete beams is the best, and it could play a “bridging” effect when the incorporation of fiber is within the load range of about 60%, which inhibited the developing speed of cracks, but with the gradual increase of the load, the “bridging” effect disappeared.
In bridge engineering, the problem of steel bar corrosion has increasingly affected the use of bridges, and the emergence of new composite materials provides an effective way for solving the problem of steel bar corrosion, that is, to replace or partly replace steel bar with new composite materials. There are many varieties of fiber composite materials, mainly including SFRP (Steel Fiber Reinforced Polymer), GFRP (Glass Fiber Reinforced Polymer), CFRP (Carbon Fiber Reinforced Polymer), and AFRP (Aramid Fiber Reinforced Polymer), among which GFRP is cheaper. The GFRP beam produced by totally replacing or partly replacing steel bar with new composite materials has become a powerful trend in the future development of structures. The incorporation of fiber can not only effectively improve the brittle failure of concrete, but also effectively control the size and development of crack defects, thus ultimately improving the mechanical properties and durability of concrete structures [
The alkali-resistant glass fiber was incorporated into the concrete to form GFRC (Glass Fiber Reinforced Concrete). The numerical simulation of four-point bending test of GFRP reinforced concrete beams with 0.0%, 0.5%, 1.0%, and 1.5% fiber volume incorporation was carried out to obtain the bearing capacity, which was compared with the calculated test values to analyze the influence of the fiber incorporation amount on the bearing capacity of GFRP reinforced concrete beam.
The experimental cement is the ordinary silicate cement with strength grade of 42.5 produced by Binzhou Qinglongshan Cement Plant, with fineness modulus of the experimental sand of 2.9, apparent density of 2710 kg/m3, bulk density of 1600 kg/m3, bulk density porosity of 45%, and stone powder content of 5.1%. The experimental stone is the ordinary concrete-used crushed stone produced in Qingzhou, Shandong, with apparent density of 2700 kg/m3, bulk density of 1420 kg/m3, crushing index of 9.9%, mud content of 0.5%, bulk density porosity of 47%, and needle-like particle content of 4%. The experimental water-reducing agent is the FMY-1 water-reducing agent produced by Binzhou Meiya Building Materials Technology Co., Ltd. The experiment water is tap water.
The experimental glass fiber is the alkali-resistant glass fiber specially used for bridge concrete provided by Taishan Fiberglass Co., Ltd., and the characteristic parameters are shown in Table
Alkali-resistant glass fiber characteristics parameters.
Length/mm | Length-to-diameter ratio | Original wire diameter/ |
Ignition loss LO/% | Moisture content MOL/% |
---|---|---|---|---|
36 | 58 | 14–19 | 0.80–2.00 | ≤0.50 |
In the table, the original wire diameter conforms to the standard of ISO1888: 2006, the ignition loss conforms to the standard of ISO1887: 1995, and the water content conforms to the standard of ISO 3344: 1997. The fiber has high zirconium content and conforms to the standards of ASTM C1666/C 1666/M-07 and EN15422, and according to PCI and GRCA, it is suggested for production. GFRP bar is provided by Nanjing Fenghui Composite Materials Co., Ltd., with diameter of 10 mm and length of 1100 mm. The mechanical properties of the experimental glass fiber bar are shown in Table
Mechanical parameters of GFRP bar.
Diameter/mm | Density/kg⋅m−3 | Extreme tensile strength/kN | Tensile strength/MPa | Elastic modulus/GPa |
---|---|---|---|---|
10 | 2200 | 72 | 980 | 42 |
According to the literature [
Fiber-concrete incorporation ratio design.
Number | Cement/kg | Coarse aggregate/kg | River sand/kg | Water/kg | Water-reducer/kg⋅m−3 | Fibers/vol.% |
---|---|---|---|---|---|---|
1# | 500 | 1045 | 700 | 200 | 3.0 | 0 |
2# | 500 | 1045 | 700 | 200 | 3.0 | 0.5 |
3# | 500 | 1045 | 700 | 200 | 3.0 | 1.0 |
4# | 500 | 1045 | 700 | 200 | 3.0 | 1.5 |
The cross-section design size of the experimental beam is 80 mm × 110 mm; the length is 1100 mm, and the thickness of the protective layer of GFRP is 30 mm, as shown in Figure
Design figure of GFRP reinforced fiber reinforced concrete beam (unit: mm).
The numerical simulation was carried out by ABAQUS finite element software, and the choice of parameters in the software simulation had great effect on the simulation results. Since there are a variety of constitutive models, and the calculation of nonlinear model has heavy workload, now there are no literatures that have made comparison and analysis on the differences between the various models. Therefore, in order to reflect the actual force process of GFRP reinforced concrete beams as much as possible, the methods of experimental research and theoretical analysis were used to analyze the constitutive model of fiber reinforced concrete in this numerical model.
Axial compression experiments were, respectively, carried out on cubic fiber reinforced concrete with fiber incorporation of 0.0%, 0.5%, 1.0%, and 1.5%, and the YAW-2000B microcomputer controlled electrohydraulic pressure experimenting machine was used as the experimental equipment. The experimental data of axial compressive strength and fiber incorporation are shown in Table
Test data of the axial compressive strength of fiber reinforced concrete.
Fiber incorporation/% | Compressive area |
Ultimate load |
Compressive strength |
---|---|---|---|
0.0 | 10000 | 48.30 | 48.30 |
0.5 | 10000 | 52.22 | 52.22 |
1.0 | 10000 | 46.50 | 46.50 |
1.5 | 10000 | 42.68 | 42.68 |
The constitutive model of the compressive stress-strain curve corresponding to the four types of fiber reinforced concrete with different fiber incorporation was sketched according to the data obtained in the experiment, as shown in Figure
Stress-strain curves of fiber reinforced concrete under uniaxial compression.
The numerical simulation of the axial tension of steel reinforced concrete was carried out, and the parameters equation given by Zhenhai and Xudong [
The cylinder splitting experiment in [
Splitting tensile strength test data of fiber reinforced concrete.
Fiber incorporation amount/% | Splitting area |
Ultimate load |
Nonstandard |
Conversion coefficient |
Splitting tensile strength |
Axial tensile strength |
Axial tensile peak strain |
Axial tensile |
Peak secant modulus |
|
---|---|---|---|---|---|---|---|---|---|---|
0.0 | 10000 | 22.91 | 2.291 | 0.85 | 1.9474 | 1.753 | 0.8801 | 25.51 | 19.92 | 1.28 |
0.5 | 10000 | 25.13 | 2.413 | 0.85 | 2.0511 | 1.846 | 0.9051 | 26.09 | 20.40 | 1.28 |
1.0 | 10000 | 24.96 | 2.496 | 0.85 | 2.1216 | 1.909 | 0.9216 | 26.48 | 20.72 | 1.28 |
1.5 | 10000 | 21.66 | 2.166 | 0.85 | 1.8411 | 1.657 | 0.8537 | 24.91 | 19.41 | 1.28 |
Splitting tensile strength test in [
Splitting tensile strength test in this experiment.
The ascending segment of the axial tensile stress-strain full curve was obtained according to the splitting tensile test data, and the descending segment of the axial tensile stress-strain full curve was obtained according to the tensile stress-strain typical curve of alkali-resistant glass fiber reinforced concrete in [
Axial tensile stress-strain full curve.
The basic input parameters of the experimental GFRP are shown in Table
GFRP stress-strain constitutive model.
The general input of the elastic modulus parameters in the numerical simulation is secant modulus, of which the secant modulus value is usually calculated by taking the secant with work stress of
Secant modulus of fiber reinforced concrete.
Fiber incorporation/% |
|
|
Simulation |
|
|
Ratio to standard value |
---|---|---|---|---|---|---|
0.0 | 48.3 | 19.32 | 0.000480 | 0.0016245 | 40250.00 | 1.24 |
0.5 | 52.22 | 20.888 | 0.000484 | 0.001691 | 43157.0248 | 1.33 |
1.0 | 46.5 | 18.6 | 0.000482 | 0.001707 | 38589.2116 | 1.19 |
1.5 | 42.68 | 17.072 | 0.000517 | 0.001946 | 33021.2766 | 1.02 |
Regression curve of the compressive stress-strain ascending segment of fiber reinforced concrete.
Due to the symmetry of the structure, in order to simplify the calculation, the numerical simulation of the GFRP fiber reinforced concrete was analyzed by taking the semistructure. The model consists of three components, steel block, GFRP, and concrete beam. The type of the boundary condition is XSYMM, that is, symmetrical boundary condition, in which the symmetry plane is the vertical plane of the axis 1, and the limited vertical displacement of the constraint type at the support is
Mesh division of GFRP fiber reinforced concrete beam model.
Through the numerical simulation of the four-point bending bearing capacity of GFRP fiber reinforced concrete beams, the key parameters such as cracking load, ultimate load, and corresponding deflection of GFRP reinforced fiber concrete beams were obtained, as seen in Table
Simulation of the four-point bending bearing capacity parameters.
Fiber content/% | Cracking load/kN | Ultimate load/kN | Cracking deflection/mm | Ultimate deflection/mm |
---|---|---|---|---|
0.0 | 2.16 | 12.88 | 0.1212 | 12.5313 |
0.5 | 2.42 | 13.34 | 0.1218 | 12.8191 |
1.0 | 2.52 | 15.34 | 0.1428 | 15.9406 |
1.5 | 2.14 | 13.06 | 0.1423 | 13.2718 |
The strain of the GFRP reinforced fiber concrete beams is seen in Figure
Strain nephogram of GFRP reinforced concrete beam.
GFRP does not have yield point, and the stresses of GFRP in the GFRP reinforced concrete beams with different amounts of fiber incorporation were obtained by numerical simulation. The maximum stress of GFRP is within the range of 360.4 MPa~369.2 MPa, which is less than the average minimum tensile stress of GFRP experiment,
In this paper, the
Trend of the
General trend of the
Trend of the loading point of the
From the simulation of the bearing capacity, the glass fiber played good “bridging” effect within the load range about 60% and inhibited the development speed of the crack, but with the increase of the load, the “bridging” effect disappeared.
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The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors would like to express appreciation for the financial support by the Natural Science Foundation of China (51178361).